8A F11 Q1 - Revision history

Matt Lee at 22:22, 6 April 2015

2015-04-06T22:22:11Z

Matt Lee at 22:01, 6 April 2015

2015-04-06T22:01:30Z

Matt Lee at 22:00, 6 April 2015

2015-04-06T22:00:31Z

Matt Lee at 22:00, 6 April 2015

2015-04-06T22:00:08Z

Matt Lee at 08:12, 26 March 2015

2015-03-26T08:12:42Z

Grad at 04:10, 21 March 2015

2015-03-21T04:10:37Z

Grad at 03:27, 21 March 2015

2015-03-21T03:27:46Z

Grad: Created page with "'''Question:''' Find $f^{-1}(x) for f(x) = \log_3(x+3)-1$ {| class="mw-collapsible mw-collapsed" style = "text-align:left;" ! Foundations |- |1) How would you fin..."

2015-03-21T03:26:47Z

Created page with "'''Question:''' Find <math>f^{-1}(x) for f(x) = \log_3(x+3)-1</math> {| class="mw-collapsible mw-collapsed" style = "text-align:left;" ! Foundations |- |1) How would you fin..."

New page

'''Question:''' Find <math>f^{-1}(x) for f(x) = \log_3(x+3)-1</math>

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! Foundations
|-
|1) How would you find the inverse for a simpler function like <math>f(x) = 3x + 5</math>?
|-
|2) How are <math>log_3(x)</math> and <math>3^x</math> related?
|-
|For 1) you would replace f(x) by y, switch x and y, and finally solve for y.
|-
|For 2) By stating <math>y = \log_3(x)</math> we also get the following relation <math>x = 3^y</math>
|}

Solution:

{| class = "mw-collapsible mw-collapsed" style = "text-align:left;"
! Step 1:
|-
|We start by replacing f(x) with y.
|-
|This leaves us with <math>y = \log_3(x + 3) - 1</math>
|}

{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
! Step 2:
|-
|Now we swap x and y to get <math>x = \log_3(y + 3) - 1</math>
|-
|In the next step we will solve for y.
|}

{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
! Step 3:
|-
|Starting with <math>x = \log_3(y + 3) - 1</math>, we start by adding 1 to both sides to get
|-
|<math>x + 1 = \log_3(y + 3).</math> Now we will use the relation in Foundations 2) to swap the log for an exponential to get
|-
|<math>y + 3 = 3^{x+1}</math>. All we have to do is subtract 3 from both sides to yield the final answer
|}

{|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
! Step 4:
|-
|After subtracting 3 from both sides we get <math>y = 3^{x+1}-3</math>. Replacing y with <math>f^{-1}(x)</math> we arrive at the final answer that
|-
|<math>f^{-1}(x) = 3^{x+1} - 3</math>
|}

← Older revision		Revision as of 22:22, 6 April 2015
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−	[[8AF11Final\|<u>'''Return to Exam</u>''']]	+	[[8AF11Final\|<u>'''Return to Sample Exam</u>''']]

← Older revision		Revision as of 22:01, 6 April 2015
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	\|}		\|}

−	[[8AF11Final\|Return to Exam]]	+	[[8AF11Final\|<u>'''Return to Exam</u>''']]

← Older revision		Revision as of 22:00, 6 April 2015
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	\|}		\|}

−	[[8AF11Final]]	+	[[8AF11Final\|Return to Exam]]

← Older revision		Revision as of 22:00, 6 April 2015
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	\|<math>f^{-1}(x) = 3^{x+1} - 3</math>		\|<math>f^{-1}(x) = 3^{x+1} - 3</math>
	\|}		\|}
		+
		+	[[8AF11Final]]

← Older revision		Revision as of 03:27, 21 March 2015
Line 1:		Line 1:
−	'''Question:''' Find <math>f^{-1}(x) for f(x) = \log_3(x+3)-1</math>	+	'''Question:''' Find <math>f^{-1}(x)</math> for <math>f(x) = \log_3(x+3)-1</math>

@@ Line 49: / Line 49: @@
 |-
 |After subtracting 3 from both sides we get <math>y = 3^{x+1}-3</math>. Replacing y with <math>f^{-1}(x)</math> we arrive at the final answer that
 |-
 |<math>f^{-1}(x) = 3^{x+1} - 3</math>
 |}

@@ Line 9: / Line 9: @@
 |2) How are <math>log_3(x)</math> and <math>3^x</math> related?
 |-
-|For 1) you would replace f(x) by y, switch x and y, and finally solve for y.
+|Answers:
 |-
-|For 2) By stating <math>y = \log_3(x)</math> we also get the following relation <math>x = 3^y</math>
+|1) you would replace f(x) by y, switch x and y, and finally solve for y.
 |}

8A F11 Q1 - Revision history

Matt Lee at 22:22, 6 April 2015

Matt Lee at 22:01, 6 April 2015

Matt Lee at 22:00, 6 April 2015

Matt Lee at 22:00, 6 April 2015

Matt Lee at 08:12, 26 March 2015

Grad at 04:10, 21 March 2015

Grad at 03:27, 21 March 2015

Grad: Created page with "'''Question:''' Find f^{-1}(x) for f(x) = \log_3(x+3)-1 {| class="mw-collapsible mw-collapsed" style = "text-align:left;" ! Foundations |- |1) How would you fin..."

Grad: Created page with "'''Question:''' Find $f^{-1}(x) for f(x) = \log_3(x+3)-1$ {| class="mw-collapsible mw-collapsed" style = "text-align:left;" ! Foundations |- |1) How would you fin..."